First Six Weeks Math Stards Sequence Grade 8 Domain Cluster Stard Dates The Number System The Number System Know that there are numbers that are not rational, approximate them by rational numbers. Know that there are numbers that are not rational, approximate them by rational numbers. radicals radicals exponents 1. Know that numbers that are not rational are called irrational. Underst informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, convert a decimal expansion which repeats eventually into a rational number 2. Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, estimate the value of expressions (e.g., π2). For example, by truncating the decimal expansion of 2, show that 2 is 1 2, then 1.4 1.5, explain how to continue on to get better approximations. 2. Use square root cube root symbols to represent solutions to equations of the form x 2 = p x 3 = p, where p is a positive rational number. Evaluate square roots of small perfect squares cube roots of small perfect cubes. Know that 2 is irrational. 1. Know properties of exponents to generate equivalent numerical expressions. For example, 32 x 3 5 = 3 3 = 1/33 = 1/27. August 15-26 August 29-Sept 2 Sept 6-14 Sept 15-21
Second Six Weeks Math Stards Sequence Grade 8 Domain Cluster Stard Dates radicals radicals Analyze solve linear equations pairs of simultaneous linear equations. Underst the connections proportional relationships, lines, linear equations. Underst the connections proportional relationships, lines, linear equations. 3. Use numbers expressed in the form of a single digit times an power of 10 to estimate very large or very small quantities, to express how many times as much one is than the other. For example, estimate the population of the United States as 3 x 108 the population of the world as 7 x 109, determine that the world population is more than 20 times larger. 4. Perform operations with numbers expressed in scientific notation, including problems where both decimal scientific notation are used. Use scientific notation choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology. 7. Solve linear equations in one variable. a. Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a b are different numbers). b. Solve linear equations with rational number coefficients, including equations whose solutions require exping expressions using the distributive property collecting like terms. 5. Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed. 6. Use similar triangles to explain why the slope m is the same any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin the equation y = mx + b for a line intercepting the vertical axis at b September 22-28 September 29- October 7 October 13-26 October 27-4 7-11
Third Six Weeks Math Stards Sequence Grade 8 Domain Cluster Stard Dates Analyze solve linear equations pairs of simultaneous linear equations. Define, evaluate, compare Define, evaluate, compare Define, evaluate compare Use to model relationships quantities. Use to model relationships quantities. 8. Analyze solve pairs of simultaneous linear equations. a. Underst that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously. b. Solve systems of two linear equations in two variables algebraically, estimate solutions by graphing the equations. Solve simple cases by inspection. For example, 3x + 2y = 5 3x + 2y = 6 have no solution because 3x + 2y cannot simultaneously be 5 6. c. Solve real-world mathematical problems leading to two linear equations in two variables. For example, given coordinates for two pairs of points, determine whether the line through the first pair of points intersects the line through the second pair. 1. Underst that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input the corresponding output.(function notation is not required in Grade 8.) 3. Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of that are not linear. For example, the function A = s2 giving the area of a square as a function of its side length is not linear because its graph contains the points (1,1), (2,4) (3,9), which are not on a straight line. 2. Compare properties of two each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a linear function represented by a table of values a linear function represented by an algebraic expression, determine which function has the greater rate of change. 4. Construct a function to model a linear relationship two quantities. Determine the rate of change initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change initial value of a linear function in terms of the situation it models, in terms of its graph or a table of values. 5. Describe qualitatively the functional relationship two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally. 14- December 2 December 5- Christmas Break
Fourth Six Weeks Math Stards Sequence Grade 8 Domain Cluster Stard Dates Underst congruence 1. Verify experimentally the properties of rotations, reflections, translations: a. Lines are taken to lines, line segments to line segments of the same length. b. Angles are taken to angles of the same measure. c. Parallel lines are taken to parallel lines. January 4-13 Underst congruence Underst congruence Underst congruence Underst congruence 2. Underst that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, translations; given two congruent figures, describe a sequence that exhibits the congruence them 3. Describe the effect of dilations, translations, rotations, reflections on two-dimensional figures using coordinates. 4. Underst that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, dilations; given two similar two dimensional figures, describe a sequence that exhibits the similarity them. 5. Use informal arguments to establish facts about the angle sum exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, the angle-angle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, give an argument in terms of transversals why this is so. Jan 16-20 Jan 23-27 Jan 30- Feb 3 Feb 6-10
Fifth Six Weeks Math Stards Sequence Grade 8 Domain Cluster Stard Dates Underst 6. Explain a proof of the its converse Feb 13-17 Statistics Probability Underst Underst Solve real-world mathematical problems involving volume of cylinders, cones spheres Investigate patterns of association in bivariate data 7. Apply the to determine unknown side lengths in right triangles in real-world mathematical problems in two three dimensions. 8. Apply the to find the distance two points in a coordinate system. 9. Know the formulas for the volumes of cones, cylinders, spheres use them to solve real-world mathematical problems. 1. Construct interpret scatter plots for bivariate measurement data to investigate patterns of association two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, nonlinear association. 2. Know that straight lines are widely used to model relationships two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, informally assess the model fit by judging the closeness of the data points to the line. 3. Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope intercept. For example, in a linear model for a biology experiment, interpret a slope of 1.5 cm/h as meaning that an additional hour of sunlight each day is associated with an additional 1.5 cm in mature plant height. 4. Underst that patterns of association can also be seen in bivariate categorical data by displaying frequencies relative frequencies in a two-way table. Construct interpret a two-way table summarizing data on two categorical variables collected from the same subjects. Use relative frequencies calculated for rows or columns to describe possible association the two variables. For example, collect data from students in your class on whether or not they have a curfew on school nights whether or not they have assigned chores at home. Is there evidence that those who have a curfew also tend to have chores? Feb 20-24 Feb 27- March 3 March 6-10 Until testing /or review time